Question 1

A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following statements is correct? A) The overall general movement of number of surfboards sold by this company is positive because the coefficients of the indicator variables are positive. B) The overall general movement of number of surfboards sold by this company is positive because the intercept is positive. C) The overall general movement of number of surfboards sold by this company is positive because the coefficient of time t is positive. D) None of these choices are correct.

Accepted Answer

The coefficient of time t is positive, indicating that the number of surfboards sold by the company is increasing over time. The coefficients of the indicator variables only show the effect of specific months on the number of surfboards sold, but do not provide information on the overall trend. The intercept being positive only indicates the expected number of surfboards sold in December 2010 and does not provide information on the overall trend.

Question 2

In determining weekly seasonal indexes for petrol consumption, the sum of the 52 means for petrol consumption as a percentage of the moving average is 5050. To get the seasonal indexes, each weekly mean is to be multiplied by:
A) 5200 / 5050.
B) (5200 + 5050) / 52.
C) (5050 + 52) / 5200.
D) 5050 / 5200.

Accepted Answer

The formula to calculate the seasonal index for any week is:

Seasonal index = (Weekly mean / Moving average) x Overall index

Given that the sum of the 52 means for petrol consumption as a percentage of the moving average is 5050, we can express the overall index as:

Overall index = Sum of the 52 means / Sum of the 52 moving averages
Overall index = 5050 / 52 = 96.92 (approximately)

To calculate the seasonal index for any week, we need to multiply the weekly mean by the overall index and then divide by the moving average. Therefore, the equation can be rearranged as:

Seasonal index = (Weekly mean x Overall index) / Moving average

We want to find a factor that we can multiply each weekly mean by to get the seasonal index. This factor should be independent of the weekly mean, but dependent on the overall index and the moving average.

If we multiply both the overall index and the moving average by a factor of 100, we can write:

Overall index (as a percentage of moving average) = (Sum of the 52 means / Sum of the 52 moving averages) x 100
Overall index (as a percentage of moving average) = (5050 / 52) x 100 = 9692

We can now express the formula for the seasonal index as:

Seasonal index = (Weekly mean / Moving average) x (9692 / 100)

Simplifying, we get:

Seasonal index = (Weekly mean x 96.92) / Moving average

Therefore, to get the seasonal indexes for all 52 weeks, we need to multiply each weekly mean by a factor of 96.92 and then divide by the moving average. We know that the sum of the 52 means as a percentage of the moving average is 5050. Therefore:

Sum of weekly means = Sum of seasonal indexes x Moving average / 96.92
5050 = Sum of seasonal indexes x Moving average / 96.92
Sum of seasonal indexes = (5050 x 96.92) / Moving average

We are looking for a factor that we can multiply each weekly mean by to get the seasonal indexes. This factor should be independent of the moving average. Therefore, we need to express the sum of seasonal indexes as a function of the sum of weekly means only. We know that the sum of weekly means is 5200 (100% x 52 weeks). Therefore:

Sum of seasonal indexes = (5200 x factor) / Moving average

Equating the two expressions for the sum of seasonal indexes, we get:

(5050 x 96.92) / Moving average = (5200 x factor) / Moving average
Factor = (5050 x 96.92) / (5200 x 100)
Factor = 0.9804 (approximately)

Therefore, to get the seasonal indexes, each weekly mean should be multiplied by 0.9804 (or, equivalently, divided by 1.0199, which is the reciprocal of 0.9804). The closest choice to this factor is A, which gives 5200 / 5050 = 1.0297, which is the reciprocal of 0.9707. However, this choice is not exact, so we need to choose the best possible answer. Choice A is the best option.

Question 3

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?
A) 0.10.
B) 0.50.
C) 0.30.
D) 0.70.

Accepted Answer

The smoothed series will catch up most quickly to changes in the original time series direction when the smoothing constant (w) is higher. A higher value of w gives more weight to the most recent observations, making the series more responsive to changes. Therefore, 0.70 will result in the quickest adjustment.

Question 4

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:
A) additive model.
B) multiplicative model.
C) moving averages model.
D) forecast model.

Accepted Answer

The additive model assumes that the time-series value at time t is the sum of four components: level, trend, seasonality, and error. This means that the values are added together rather than multiplied or moving averages being taken. Therefore, the correct choice is A.

Question 5

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $=6.8+1.2 t$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:
A) 34.40.
B) 27.52.
C) 43.00.
D) 35.65.

Accepted Answer

The answer of The trend equation for quarterly sales data...

Question 6

The results of a quadratic model fit to time-series data were ?_t = 7.5 -0.2t + 2.8t², where t = 1 for 2002. The forecast value for 2011 is: A) 289.5. B) 285.5. C) 236.1. D) 232.5.

Accepted Answer

To find the forecasted value for 2011, substitute t = 10 into the given equation: ŷ_t = 7.5 F1F1F1S1F1F1F10 0.2(10) + 2.8(10)² ŷ_t = 285.5 Therefore, the forecasted value for 2011 is 285.5. The correct answer is B.

Question 7

A time series regression equation measuring the number of surfboards sold by a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following statements is correct? A) There is a mistake with this regression model because all the coefficients of the indicator variables are positive. B) There is no indicator variable for the June quarter in this model because there is no seasonal effect in June due to winter in Australia. C) There is a mistake with this model because the indicator variable for the June quarter has been left out. D) There is no indicator variable for the June quarter in this model because we need one less indicator variable than number of categories to use indicator variables with regression for a time series.

Accepted Answer

The answer of A time series regression equation measuring the...

Question 8

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:
A) trend and cyclical components.
B) cyclical and seasonal components.
C) seasonal and random variation components.
D) four components.

Accepted Answer

The answer of Of the four components of the multiplicative...

Question 9

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?
A) 0.40.
B) 0.48.
C) 0.43.
D) 0.37.

Accepted Answer

The higher the smoothing constant, the more rapidly the smoothing method reacts to changes in the time-series data. Among the given options, 0.48 is the highest, causing the most rapid reaction.

Question 10

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?
A) The autoregressive model.
B) The linear model for long-term trend.
C) The quadratic model for long-term trend.
D) All of these choices are correct.

Accepted Answer

The quadratic model for long-term trend is the best choice because it allows for a rapid early growth rate followed by a levelling-off or eventual saturation. The autoregressive model and linear model for long-term trend may not fully capture this pattern.

Question 11

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:
A) trend component.
B) cyclical component.
C) seasonal component.
D) random variation component.

Accepted Answer

Smoothing time series data, whether by moving average or exponential smoothing methods, is primarily aimed at reducing the impact of the random variation component. These techniques help in filtering out the noise to better identify the underlying pattern in the data.

Question 12

One measure of the accuracy of a forecasting model is the:
A) deseasonalised time series.
B) four-period moving average.
C) mean absolute deviation.
D) smoothing constant.

Accepted Answer

The mean absolute deviation is a common measure of forecasting accuracy that reflects the average magnitude of the forecast errors. It is calculated by taking the absolute value of the difference between the actual values and the forecast values, and then averaging those absolute values. The smaller the mean absolute deviation, the more accurate the forecasting model. The other options listed are not measures of forecasting accuracy.

Question 13

The model that assumes the time-series value at time t is the product of the four time-series components is referred to as the:
A) additive model.
B) forecast model.
C) moving averages model.
D) multiplicative model.

Accepted Answer

The statement describes the multiplicative model, where the time-series value at time t is the product of the four time-series components: trend, seasonality, cyclical, and random error. The additive model assumes that the time-series value at time t is the sum of the four time-series components. Moving averages model and forecast model are specific techniques used within time-series analysis but are not the same as the overall model assumption.

Question 14

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:
A) 24 months.
B) 12 months.
C) 6 months.
D) 3 months.

Accepted Answer

A centred moving average with a period of 12 months takes into account the seasonal fluctuations over a full year, making it the best choice for determining monthly seasonal indexes.

Question 15

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:
A) lowest MAD and highest SSE.
B) highest MAD and lowest SSE.
C) lowest MAD and SSE.
D) highest MAD and SSE.

Accepted Answer

The model that forecasts the data best will have the lowest MAD and SSE. MAD measures the average absolute difference between actual and predicted values, while SSE measures the sum of squared differences between actual and predicted values. Lower values for both measures indicate a better fit between the model and the data. Therefore, the answer is choice C, which has the lowest values for both MAD and SSE.

Question 16

The regression trend line for annual energy consumption for 1985-2005 is given by ŷ_t = 70 + 0.53t, where t = 1 for 1985. If the annual energy consumption for 2000 was 82.5, then the percentage of trend for 2000 was: A) 105.122%. B) 95.127%. C) 104.321%. D) 98.462%.

Accepted Answer

The answer of The regression trend line for annual energy...

Question 17

Which of the following is true?
A) In trend analysis, the independent variable is time only if the equation is linear.
B) The number of time periods in a centred moving average is always even.
C) If the seasonal index for December sales is 120, this means that December sales tend to be 120% higher than the 'average' month.
D) The cyclical component of a time series refers to repeating patterns that have a period of a year or less.

Accepted Answer

A seasonal index of 120 means that December sales are 20% higher than the average month, not 120% higher. The other options are incorrect as well.

Question 18

The trend equation for annual sales data (in millions of dollars) is $=65+2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:
A) 90.0.
B) 7.28.
C) 7.50.
D) 7.69.

Accepted Answer

The answer of The trend equation for annual sales data...

Question 19

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by:
A) 1200 / 1230.
B) 1230 / 1200.
C) (1230 + 1200) / 2.
D) (1230 + 1200) / 12.

Accepted Answer

To normalize the seasonal indexes so that their sum equals 1200 (100% for each month), each mean should be multiplied by 1200 / 1230 to adjust the total sum from 1230 to 1200.

Question 20

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?
A) Trend.
B) Cyclical.
C) Seasonal.
D) Random variation.

Accepted Answer

The answer of The high level of airline ticket sales...

Quiz 23: Time-Series Analysis and Forecasting

In determining weekly seasonal indexes for petrol consumption, the sum of the 52 means for petrol consumption as a percentage of the moving average is 5050. To get the seasonal indexes, each weekly mean is to be multiplied by:

For which of the following values of the smoothing constant w will the smoothed series catch up most quickly whenever the original time series changes direction?

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is =6.8+1.2t=6.8+1.2 t=6.8+1.2t , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:

The results of a quadratic model fit to time-series data were ?t = 7.5 -0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

Of the four components of the multiplicative time-series model, the ratio of the time series to the moving average isolates the:

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?

Which of the following models might be appropriate to describe a new product that has experienced a rapid early growth rate followed by the inevitable levelling-off?

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

One measure of the accuracy of a forecasting model is the:

The model that assumes the time-series value at time t is the product of the four time-series components is referred to as the:

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

The regression trend line for annual energy consumption for 1985-2005 is given by ŷt = 70 + 0.53t, where t = 1 for 1985. If the annual energy consumption for 2000 was 82.5, then the percentage of trend for 2000 was:

Which of the following is true?

The trend equation for annual sales data (in millions of dollars) is =65+2.5t=65+2.5 t=65+2.5t , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

In determining monthly seasonal indexes for petrol consumption, the sum of the 12 means for petrol consumption as a percentage of the moving average is 1230. To get the seasonal indexes, each of the 12 monthly means is to be multiplied by:

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $=6.8+1.2 t$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:

The results of a quadratic model fit to time-series data were ?_t = 7.5 -0.2t + 2.8t², where t = 1 for 2002. The forecast value for 2011 is:

The regression trend line for annual energy consumption for 1985-2005 is given by ŷ_t = 70 + 0.53t, where t = 1 for 1985. If the annual energy consumption for 2000 was 82.5, then the percentage of trend for 2000 was:

The trend equation for annual sales data (in millions of dollars) is $=65+2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is: